Various objects and systems in intransitive relations of superiority (“rock-paper-scissors”
relations) are described (intransitive sets of sticks, dice, chess positions, machines …

The status of the axioms of transitivity of dominance (“if x dominates y and y dominates z,
then x dominates z” and “if a person prefers A to B and B to C, then that person should prefer …

Positions of chess players in intransitive (rock-paper-scissors) relations are considered.
Namely, position A of White is preferable (it should be chosen if choice is possible) to …

We settle a version of the conjecture about intransitive dice posed by Conrey, Gabbard,
Grant, Liu and Morrison in 2016 and Polymath in 2017. We consider generalized dice with …

An important and interesting phenomenon of the last few decades is the increasing number
of mathematical studies of so-called intransitive dice with non-standard numbers on their …

It has been shown that a structure of mutual wins of 3 nontransitive dice (with numbers equal
to numbers from The Lo Shu magic square) can be repeated at least twice in different …

76 АН Поддьяков оценок–фиксированных чисел в каком-либо абсолютном рейтинге, не
учитывающем в явном виде позицию другой стороны. Для нетранзитивных позиций …

Jan-ken, aka rock-paper-scissors, is a cerebrated example of a non-transitive game with
three (pure) strategies, rock, paper and scissors. Interestingly, any Jan-ken generalized to …

Nontransitive dice are dice beating one another in a cyclic way: die A wins die B, B wins C,
and C wins A (like in a rock-paper-scissors game). In this article, it has been shown that a …

Motivated by classical nontransitivity paradoxes, we call an n-tuple (x 1,…, xn)∈[0, 1] n
cyclic if there exist independent random variables U 1,…, U n with P (U i= U j)= 0 for i≠ j …